Where is the Word document located?
For the Word document that will not open in Pages, click once on that reluctant Word document in the Finder, and press command+i (Get Info). What is shown for the creation date? Word documents older than circa 2001 will be rejected by Pages, TextEdit, and Preview with "document name" can't be opened right now. Pages couldn't read the file. That message was from a Word .doc from 1995 (which I keep to produce this message).
Always share what specific version of Pages you are using via Pages : About Pages. It should be Pages v8.2 on Catalina. Sometimes a reboot of the Mac has been known to resolve this failure to open documents in Catalina, and certainly booting into Safe Boot mode can't hurt either. Be certain to reboot normally from Safe Boot mode.
Another approach would be to install the free LibreOffice Suite, and see if it can open the Word document. As it is an MS Office Suite clone, it will open things that neither Pages nor Word can open. Resaving them is often all that is needed to allow Pages and Word to open the document normally. I always keep a current version of LibreOffice handy for this very rescue purpose.
LibreOffice installs entirely into your /Applications folder. Because it is from outside the Mac App Store, you will need to control-click on the application itself, and choose Open. A brief validation process will occur, followed by another dialog panel. Click Open on it too, and you do not have to repeat this ritual, as LibreOffice will now launch normally.